Transmission modes and signaling for uplink MIMO support or single TB dual-layer transmission in LTE uplink

ABSTRACT

An apparatus for mapping data in a wireless communication system. The apparatus includes circuitry for generating a precoding matrix for multi-antenna transmission based on a precoding matrix indicator (PMI) feedback from at least one remote receiver where the PMI indicates a choice of precoding matrix derived from a matrix multiplication of two matrices from a first code book and a second codebook. The apparatus further includes circuitry for precoding one or more layers of a data stream with the precoding matrix and transmitting the precoded layers of data stream to the remote receiver.

CLAIM OF PRIORITY

This application is a Continuation of application Ser. No. 14/503,083filed Sep. 30, 2014, which is a Continuation of application Ser. No.13/098,967 filed May 2, 2011, now U.S. Pat. No. 8,848,817 B2, whichclaims priority under 35 U.S.C. 119(e)(1) to U.S. ProvisionalApplication No. 61/329,864 flied Apr. 30, 2010, U.S. ProvisionalApplication No. 61/331,466 filed May 5, 2010, U.S. ProvisionalApplication No. 61/351,061 filed Jun. 3, 2010 U.S. ProvisionalApplication No. 61/355,850 filed Jun. 17, 2010, U.S. ProvisionalApplication No. 61/357,382 filed Jun. 22, 2010, U.S. ProvisionalApplication No. 61/364,671 filed Jul. 15, 2010, U.S. ProvisionalApplication No. 61/369,369 filed Jul. 30, 2010, and U.S. ProvisionalApplication No. 61/372,608 filed Aug. 11, 2010.

TECHNICAL FIELD OF THE INVENTION

The technical field of this invention is wireless communication such aswireless telephony.

BACKGROUND OF THE INVENTION

The present embodiments relate to wireless communication systems and,more particularly, to the precoding of Physical Downlink Shared Channel(PDSCH) data and dedicated reference signals with codebook-basedfeedback for multi-input multi-output (MIMO) transmissions.

With Orthogonal Frequency Division Multiplexing (OFDM), multiple symbolsare transmitted on multiple carriers that are spaced apart to provideorthogonality. An OFDM modulator typically takes data symbols into aserial-to-parallel converter, and the output of the serial-to-parallelconverter is considered as frequency domain data symbols. The frequencydomain tones at either edge of the band may be set to zero and arecalled guard tones. These guard tones allow the OFDM signal to fit intoan appropriate spectral mask. Some of the frequency domain tones are setto values which will be known at the receiver. Among these areCell-specific Channel State Information Reference Signals (CSI-RS) andDedicated or Demodulating Reference Signals (DMRS). These referencesignals are useful for channel estimation at the receiver. In amulti-input multi-output (MIMO) communication systems with multipletransmit/receive antennas, the data transmission is performed viaprecoding. Here, precoding refers to a linear (matrix) transformation ofa L-stream data into P-stream where L denotes the number of layers (alsotermed the transmission rank) and P denotes the number of transmitantennas. With the use of dedicated (user-specific) DMRS, a transmitter(base station, also termed eNodeB can perform any precoding operationwhich is transparent to a user equipment (UE) which acts as a receiver.At the same time, it is beneficial for the base station to obtain arecommendation on the choice of precoding matrix from the userequipment. This is particularly the case for frequency-divisionduplexing (FDD) where the uplink and downlink channels occupy differentparts of the frequency bands, i.e. the uplink and downlink are notreciprocal. Hence, a codebook-based feedback from the UE to the eNodeBis preferred. To enable a codebook-based feedback, a precoding codebookneeds to be designed.

The Rel. 8 Long-Term Evolution (LTE) specification includes a codebookfor 2-antenna transmissions and a codebook for 4-antenna transmissions.While those codebooks are designed efficiently, they do not supporttransmissions with 8 antennas. Moreover, it is possible to furtherimprove the performance of 4-antenna transmissions under differentscenarios such as dual-polarized antenna arrays.

While the preceding approaches provide steady improvements in wirelesscommunications, the present inventors recognize that still furtherimprovements in downlink (DL) spectral efficiency are possible.Accordingly, the preferred embodiments described below are directedtoward these problems as well as improving upon the prior art.

SUMMARY OF THE INVENTION

This invention is a method of mapping data in a wireless communicationsystem. The method includes forming a first frame having pluralpositions at a first transmitter. The first frame has a first pluralityof reference signals. A second frame having plural positionscorresponding to the plural positions of the first frame is formed at asecond transmitter remote from the first transmitter. The second framehas a second plurality of reference signals. A plurality of data signalsis inserted into the first frame at positions that are not occupied byeither the first or second plurality of reference signals. The pluralityof data signals is inserted into the second frame at positions that arenot occupied by either the first or second plurality of referencesignals. The first and second frames are transmitted to a remotereceiver.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of this invention are illustrated in thedrawings, in which:

FIG. 1 illustrates an exemplary prior art wireless communication systemto which this application is applicable;

FIG. 2 shows the Evolved Universal Terrestrial Radio Access (E-UTRA)Time Division Duplex (TDD) frame structure of the prior art;

FIG. 3 is a simplified block diagram describing a precoder selectionmechanism at the receiver (UE) based on the dual-stage codebook;

FIG. 4 shows some examples of configuration for 8-antenna array (a)array of ULA pairs (b) dual-polarized array;

FIG. 5 is an example of reporting configuration where the first PMI(PMI₁) is reported together with RI and separately from the second PMI(PMI₂);

FIG. 6 is an example of reporting configuration where the first PMI(PMI₁) is reported together with the second PMI (PMI₂) and separatelyfrom RI;

FIG. 7 is an example of reporting configuration where the first PMI(PMI₁) and the second PHI (PMI₂) are reported separately from each otherand from RI; and

FIG. 8 is a block diagram illustrating internal details of a basestation and a mobile user equipment in the network system of FIG. 1suitable for implementing this invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

FIG. 1 shows an exemplary wireless telecommunications network 100. Theillustrative telecommunications network includes base stations 101, 102and 103, though in operation, a telecommunications network necessarilyincludes many more base stations. Each of base stations 101, 102 and 103(eNB) are operable over corresponding coverage areas 104, 105 and 106.Each base station's coverage area is further divided into cells. In theillustrated network, each base station's coverage area is divided intothree cells. Handset or other user equipment (UE) 109 is shown in Cell A108. Cell A 108 is within coverage area 104 of base station 101. Basestation 101 transmits to and receives transmissions from UE 109. As UE109 moves out of Cell A 108 and into Cell B 107, UE 109 may be handedover to base station 102. Because UE 109 is synchronized with basestation 101, UE 109 can employ non-synchronized random access toinitiate handover to base station 102.

Non-synchronized UE 109 also employs non-synchronous random access torequest allocation of up-link 111 time or frequency or code resources.If UE 109 has data ready for transmission, which may be traffic data,measurements report, tracking area update, UE 109 can transmit a randomaccess signal on up-link 111. The random access signal notifies basestation 101 that UE 109 requires up-link resources to transmit the UEsdata. Base station 101 responds by transmitting to UE 109 via down-link110, a message containing the parameters of the resources allocated forUE 109 up-link transmission along with a possible timing errorcorrection. After receiving the resource allocation and a possibletiming advance message transmitted on down-link 110 by base station 101,UE 109 optionally adjusts its transmit timing and transmits the data onup-link 111 employing the allotted resources during the prescribed timeinterval.

Base station 101 configures UE 109 for periodic uplink soundingreference signal (SRS) transmission. Base station 101 estimates uplinkchannel quality information (CSI) from the SRS transmission.

FIG. 2 shows the Evolved Universal Terrestrial Radio Access (E-UTRA)time division duplex (TDD) Frame Structure. Different subframes areallocated for downlink (DL) or uplink (UL) transmissions. Table 1 showsapplicable DL/UL subframe allocations.

TABLE 1 Config- Switch-point Sub-frame number uration periodicity 0 1 23 4 5 6 7 8 9 0  5 ms D S U U U D S U U U 1  5 ms D S U U D D S U U D 2 5 ms D S U D D D S U D D 3 10 ms D S U U U D D D D D 4 10 ms D S U U DD D D D D 5 10 ms D S U D D D D D D D 6 10 ms D S U U U D S U U D

The preferred embodiments of the present invention provide improvedcommunication through precoded multi-antenna transmission withcodebook-based feedback. In a cellular communication system a userequipment (UE) is uniquely connected to and served by a single cellularbase station (eNB) at a given time. An example of such system is the3GPP Long-Term Evolution (LTE) which includes the LTE-Advanced (LTE-A)system. With increasing number of transmit antennas at the eNB, the taskof designing an efficient codebook with desirable properties ischallenging. This set of properties includes the following for8-antenna-port (termed 8 Tx) system.

(1) Applicability for several relevant antenna setups and spatialchannel conditions. Relevant 8 Tx antenna setups typically result in astructured spatial covariance matrix which is a long-term channelstatistics. Some relevant antenna setups for 8 Tx include: Uniformlinear array (ULA) with L/2 (half wavelength) spacing; 4 dual-polarizedelements with L/2 spacing between two elements; and 4 dual-polarizedelements with 4 L (larger) spacing between two elements

(2) Applicability for both Single User Multiple Input, Multiple Output(SU-MIMO) and Multiple User Multiple Input, Multiple Output (MU-MIMO).

(3) Finite alphabet whereby each matrix element belongs to a finite setof values or constellation such as Quadrature Phase Shift Keying (QPSK)or Phase Shift Keying (8PSK) alphabet.

(4) Constant modulus where all elements in a precoding matrix have thesame magnitude. This ensures power amplifier (PA) balance property inall scenarios.

(5) Nested property where every matrix/vector of rank-n is a sub-matrixof a rank-(n+1) precoding matrix, n=1, 2, . . . N−1 where N is themaximum number of layers.

(6) The associated signaling overhead should be minimized especially UEfeedback.

A precoding structure that fulfills properties 1 and 2 separates thelong-term and short-term components of the precoder. Long-term andshort-term refer to the need for feedback interval or time granularitywhich may be associated with frequency granularity as well. Thelong-term component does not need high frequency granularity while theshort-term component may need higher frequency granularity. A particularstructure of interest known as a dual-stage precoder is as follows:W=f(W ₁ ,W ₂)  (1)where: W₁ is the long-term component; and W₂ is the short-termcomponent. Each component is assigned a codebook. Thus two distinctcodebooks CB₁ and CB₂ are needed. W₁ adapts to the long-term channelstatistics such as the spatial covariance matrix. W₂ adapts to theshort-term channel properties such as phase adjustment needed tocounteract short-term fading. For this structure the feedback overheadcan be potentially reduced as compared to a one-stage counterpart sinceW₁ does not need to be updated as often as W₂. An example of the matrixfunction f(.,.) includes a product (matrix multiplication) functionf(x,y)=xy or the Kronecker product function f(x,y)=x{circle around(x)}y. The dual-stage representation in (1) can be thought as amultiple-codebook design where:

(1) A set of N codebooks {W₁ ⁽⁰⁾, W₁ ⁽¹⁾, . . . , W₁ ^((N−1))} aredefined where one codebook is selected out of the N codebooks in along-term basis. This (first) codebook is represented by W₁ in equation(1). The choice of W₁ is enumerated by a precoding matrix indicator PMI₁where PMI₁∈0, 1, . . . ,N−1).

(2) The short-term precoding matrix/vector is then derived from thechosen codebook via a short-term operation. The short-term operation isrepresented by W₂ in (1). Note that W₂ can be as simple as selecting asub-matrix of W₁ or performing linear combining across a subset ofcolumn vectors of W₁. In this case, all possible W₂ matrices/vectors(for a given W₁) formed a second codebook CB₂. For an efficient design,the second codebook CB₂ is made dependent on the choice of the firstcodebook W₁. The choice of W₂ is enumerated by a precoding matrixindicator PMI₂ where PMI₂∈{0, 1, . . . ,M₂−1} where M₂=|CB₂(PMI₁)|.Notice the dependence of CB₂ on PMI₁.

FIG. 3 illustrates the precoding matrix/vector selection process. Thefinal precoding matrix/vector is a function of two PMIs:W=f(PMI₁,PMI₂)  (2)where: PMI₁ is updated at a significantly less frequent rate than PMI₂.PMI₁ is intended for the entire system bandwidth while PMI₂ can befrequency-selective.

FIG. 3 illustrates the technique used in downlink LTE-Advanced (LTE-A).The UE selects PMI₁ and PMI₂ and hence W₁ and W₂ in a manner similar tothe LTE feedback paradigm.

The UE first selects the first precoder codebook W₁ (block 311) based onthe long-term channel properties such as spatial covariance matrix suchas in a spatial correlation domain from an input of PMI₁. This is donein a long-term basis consistent with the fact that spatial covariancematrix needs to be estimated over a long period of time and in awideband manner.

Conditioned upon W₁, the UE selects W₂ based on the short-term(instantaneous) channel. This is a two stage process. Block 312 selectsone of a set of codebooks CB₂ ⁽⁰⁾ to CB₂ ^((N−1)) based upon the PMI₁input. Block 313 selects one precoder corresponding to the selectedcodebook CB₂ ^((PMI) ¹ ⁾ and PMI₂. This selection may be conditionedupon the selected rank indicator (RI). Alternatively, RI can be selectedjointly with W₂. Block 314 takes the selected W_(L) and W₂ and forms thefunction f(W₁, W₂).

PMI₁ and PMI₂ are reported to the base station (eNodeB or eNB) atdifferent rates and/or different frequency resolutions.

Based on this design framework, several types of codebook design aredescribed. While each type can stand alone, it is also possible to usedifferent types in a single codebook design especially if the design isintended for different scenarios. A simple yet versatile design can bedevised as follows:

PMI₁ selects one of the N codebooks W₁ as indicated above.

PMI₂ selects at least one of the column vectors of W₁. The number ofselected column vectors is essentially the recommended transmission rank(RI).

This design allows construction of N different scenarios where thecodebook W₁ for each scenario is chosen to contain a set of basisvectors for a particular spatial channel characteristic W₂. While anytwo-dimensional function can be used in equation (2), the patentapplication assumes a product (matrix multiplication) functionf(x,y)=xy. Thus the final short-term precoding matrix/vector is computedas a matrix product of W₁ and W₂: W=W₁W₂.

Consider an embodiment of a dual-codebook design for 8 Tx ULA with L/2spacing at the transmitter (eNB). For this particular antenna setup, aset of discrete Fourier transform (DFT) vectors forms a complete basisand hence serves as a good codebook. The following construction forrank-1 transmission can be used:

$\begin{matrix}{{W_{1} = {\frac{1}{2\sqrt{2}}\begin{bmatrix}1 & 1 & \ldots & 1 \\1 & e^{j\frac{2\pi}{8}} & \ldots & e^{{j{(7)}}\frac{2\pi}{8}} \\\vdots & \vdots & \ddots & \vdots \\1 & e^{{j{(7)}}\frac{2\pi}{8}} & \ldots & e^{{j{(7)}}{(7)}\frac{2\pi}{8}}\end{bmatrix}}},{{CB}_{2} = \left\{ {\begin{bmatrix}1 \\0 \\\vdots \\0\end{bmatrix},\begin{bmatrix}0 \\1 \\\vdots \\0\end{bmatrix},\ldots\mspace{14mu},\begin{bmatrix}0 \\0 \\\vdots \\1\end{bmatrix}} \right\}}} & (3)\end{matrix}$Here N−1 thus having no need for PMI₁. CB₂ consists of 8 selectionvectors which imply at least 3 bits of signaling for PMI₂. For higherranks, CB₂ represents group selection. For example CB₂ for rank-2 mayinclude all or a subset of the twenty eight possible 8×2 group selectionmatrices which selects 2 out of 8 beams.

This represents the critically-sampled DFT vectors. Generally it isbeneficial to use oversampled DFT vectors especially for MU-MIMO orspace-division multiple access (SDMA) applications. While a design withN=1 with 8×8n matrix W₁, where n is the oversampling factor, ispossible, overhead reduction for updating W₂ can be obtained bypartitioning the 8n DFT vectors into multiple W₁ matrices. Suchpartitioning uses the fact that the direction of arrival (DoA) variesquite slowly for each UE. With n=4 resulting in a total of 32 DFTvectors and keeping the size of W₁ as 8×8, the following constructioncan be used:

$\begin{matrix}{W_{1}^{(n)} = {\frac{1}{2\sqrt{2}} \times \begin{bmatrix}1 & 0 & \ldots & 0 \\1 & e^{{j{(8)}}\frac{2\pi}{{(8)}{(4)}}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & e^{{j{(7)}}{(8)}\frac{2\pi}{{(8)}{(4)}}n}\end{bmatrix}{\quad{\begin{bmatrix}1 & 1 & \ldots & 1 \\1 & e^{j\frac{2\pi}{{(8)}{(4)}}} & \ldots & e^{{j{(7)}}\frac{2\pi}{{(8)}{(4)}}} \\\vdots & \vdots & \ddots & \vdots \\1 & e^{{j{(7)}}\frac{2\pi}{{(8)}{(4)}}} & \ldots & e^{{j{(7)}}{(7)}\frac{2\pi}{{(8)}{(4)}}}\end{bmatrix},\mspace{20mu}{n = 0},1,2,3,\mspace{76mu}\mspace{20mu}{{CB}_{2} = \left\{ {\begin{bmatrix}1 \\0 \\\vdots \\0\end{bmatrix},\begin{bmatrix}0 \\1 \\\vdots \\0\end{bmatrix},\ldots\mspace{14mu},\begin{bmatrix}0 \\0 \\\vdots \\1\end{bmatrix}} \right\}}}}}} & (4)\end{matrix}$Here CB₂ (size-8) is the same for different W₁ matrices. In this caseN=4. The selection of W₁ is indicated by PMI₁ which requires a 2-bitsignaling. This divides the DoA space into 4 partitions.

Partition 1 (n=0): DoA=(0, 22.5, 45, 67.5) in degrees,

Partition 2 (n=1): DoA=(90, 112.5, 135, 157) in degrees,

Partition 3 (n=2): DoA=(180, 202.5, 225, 247.5) in degrees, and

Partition 4 (n=3): DoA=(270, 292.5, 315, 337.5) in degrees.

A total of 32 length-8 vectors are obtained from {W₁ ⁽⁰⁾, W₁ ⁽¹⁾, W₁⁽²⁾, W₁ ⁽³⁾} which amounts to oversampling the 8-dimensional angle spaceby a factor of 4. It is possible to synthesize each of the 32 vectorsfrom the 8-DFT matrix used in equation (3) as the 8 orthonormal columnvectors in the 8-DFT matrix form a complete basis for 8-dimensionalcomplex-valued space. This is be achieved by choosing W₂ accordingly.This minimizes the number of W₁, but it increases the required number W₂vectors. This increase goes against the purpose of saving the short-termfeedback overhead incurred by W₂.

This construction divides the DoA space into 4 partitions. Each UE mayupdate PMI₁ and thus W₁ at a lower rate as the DoA region in which eachUE resides changes slowly. The precise DoA may change at a faster rate.This is adapted with the change of W₂.

This construction can be generalized to any oversampling factor n andany number of partitions. A design with n=2 resulting in a total of 16DFT vectors is shown in equation (4b). In this case N=2. The selectionof W₁ is indicated by PMI₁ which requires 1-bit signaling. This dividesthe DoA space into 2 partitions.

Partition 1 (n=0): DoA=(0, 22.5, 45, 67.5, 90, 112.5, 135, 157.5) indegrees, and

Partition 2 (n−1): DoA=(180, 202.5, 225, 247.5, 270, 292.5, 315, 337.5)in degrees.

$\begin{matrix}{W_{1}^{(n)} = {\frac{1}{2\sqrt{2}} \times \begin{bmatrix}1 & 0 & \ldots & 0 \\0 & e^{{j{(8)}}\frac{2\pi}{{(8)}{(2)}}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & e^{{j{(7)}}{(8)}\frac{2\pi}{{(8)}{(4)}}n}\end{bmatrix}{\quad{\begin{bmatrix}1 & 1 & \ldots & 1 \\1 & e^{j\frac{2\pi}{{(8)}{(2)}}} & \ldots & e^{{j{(7)}}\frac{2\pi}{{(8)}{(2)}}} \\\vdots & \vdots & \ddots & \vdots \\1 & e^{{j{(7)}}\frac{2\pi}{{(8)}{(2)}}} & \ldots & e^{{j{(7)}}{(7)}\frac{2\pi}{{(8)}{(2)}}}\end{bmatrix},\mspace{20mu}{n = 0},1,\mspace{45mu}\mspace{20mu}{{CB}_{2} = \left\{ {\begin{bmatrix}1 \\0 \\\vdots \\0\end{bmatrix},\begin{bmatrix}0 \\1 \\\vdots \\0\end{bmatrix},\ldots\mspace{14mu},\begin{bmatrix}0 \\0 \\\vdots \\1\end{bmatrix}} \right\}}}}}} & \left( {4b} \right)\end{matrix}$Instead of dividing the DoA space into several DoA-contiguouspartitions, it is possible to divide the DoA space into N comb-likepartitions as shown in equation (5).

$\begin{matrix}{{W_{1}^{(n)} = {{\frac{1}{2\sqrt{2}}\begin{bmatrix}1 & 0 & \ldots & 0 \\0 & e^{j\frac{\pi\; n}{4N}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & e^{j\; 7\frac{{\pi\; n}\;}{4N}}\end{bmatrix}}\begin{bmatrix}1 & 1 & \ldots & 1 \\1 & e^{j\frac{2\pi}{8}} & \ldots & e^{{j{(7)}}\frac{2\pi}{8}} \\\vdots & \vdots & \ddots & \vdots \\1 & e^{{j{(7)}}\frac{2\pi}{8}} & \ldots & e^{{j{(7)}}{(7)}\frac{2\pi}{8}}\end{bmatrix}}},\mspace{20mu}{n = 0},1,\ldots\mspace{14mu},{N - 1}} & (5)\end{matrix}$With N=2 this results in the following 2 partitions:

Partition 1: DoA=(0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4) in radians,and

Partition 1: DoA=π/8+(0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4) inradians.

One of the drawbacks of this design is the need for higher update rateof PMI₁ because a slight change of DoA over time requires updating W₁.Unless W₁ is updated at the same rate as W₂ the short-term adaptation,this design may not be preferred from overhead perspective.

When using this design for higher ranks, the same set or different setsof W₁ matrices can be used as codebook CB₁ for different ranks.Regardless, there are several possible schemes that can be used toconstruct higher-rank precoding matrices from these W₁ constructions.Some schemes include construction based on group selection of thecolumns of W₁. For W₁ of size 8×M, CB₂ for rank-2 consists of all or asubset of the M*(M−1)/2 possible Mx2 group selection matrices whichselects 2 out of M beams. This is possible, but the composite precodingmatrix W is preferably unitary to ensure constant output power. Thiscannot be guaranteed for any W₁ matrix unless W₁ is also unitary. Aprecoding matrix for higher rank can be constructed only from orthogonalcolumn vectors of W₁. For example take the rank-1 construction inequation (4b) where M=8. For a given W₁ and one of its column vectors v,there are 3 other column vectors that are orthogonal to v. Table 2 showsthis in terms of beam angle θ where the corresponding length-8 vectoris:

$\begin{matrix}{{v(\theta)} = {\frac{1}{2\sqrt{2}} \times \begin{bmatrix}1 & e^{j\;\theta} & e^{j\; 2\;\theta} & e^{j\; 3\;\theta} & e^{j\; 4\theta} & e^{j\; 5\;\theta} & e^{j\; 6\theta} & e^{j\; 7\theta}\end{bmatrix}^{T}}} & (5)\end{matrix}$It is possible to may construct the higher rank codebooks up to rank-4while ensuring the composite precoding matrix is unitary. A nestedproperty can also be enforced. The following rank-2 design can be used.The vector v(θ) corresponding to the beam angle θ in second column ofTable 2 represents the first column of the composite precoding matrix W.If the column ordering of W which represents ordering across layers isconsidered a redundancy and hence not considered in generating distinctprecoding matrices and not incorporated into the codebook design, than agiven W₁ allows 3+3+2+2+1+1+0+0 or 12 distinct rank-2 precoding matrixW. The size-12 codebook resulting from a given W₁ or n is given by:

$\begin{Bmatrix}\begin{matrix}\begin{matrix}\begin{matrix}{\begin{bmatrix}{v(0)} & {v\left( \frac{\pi}{4} \right)}\end{bmatrix},} & {\begin{bmatrix}{v(0)} & {v\left( \frac{\pi}{2} \right)}\end{bmatrix},} & {\begin{bmatrix}{v(0)} & {v\left( \frac{3\pi}{4} \right)}\end{bmatrix},}\end{matrix} \\\begin{matrix}{\begin{bmatrix}{v\left( \frac{\pi}{8} \right)} & {v\left( \frac{3\pi}{8} \right)}\end{bmatrix},} & {\begin{bmatrix}{v\left( \frac{\pi}{8} \right)} & {v\left( \frac{5\pi}{8} \right)}\end{bmatrix},} & {\begin{bmatrix}{v\left( \frac{\pi}{8} \right)} & {v\left( \frac{7\pi}{8} \right)}\end{bmatrix},}\end{matrix}\end{matrix} \\\begin{matrix}{\left\lbrack {{v\left( \frac{\pi}{4} \right)},\;\left( \frac{\pi}{2} \right)} \right\rbrack,} & {\left\lbrack {{v\left( \frac{\pi}{4} \right)}\mspace{20mu}{v\left( \frac{3\pi}{4} \right)}} \right\rbrack,\left\lbrack {{v\left( \frac{3\pi}{8} \right)}\mspace{14mu}{v\left( \frac{5\pi}{8} \right)}} \right\rbrack,}\end{matrix}\end{matrix} \\\begin{matrix}{\begin{bmatrix}{v\left( \frac{3\pi}{8} \right)} & {v\left( \frac{7\pi}{8} \right)}\end{bmatrix},} & {\begin{bmatrix}{v\left( \frac{\pi}{2} \right)} & {v\left( \frac{3\pi}{4} \right)}\end{bmatrix},} & {\begin{bmatrix}{v\left( \frac{5\pi}{8} \right)} & {v\left( \frac{7\pi}{8} \right)}\end{bmatrix},}\end{matrix}\end{Bmatrix}$For W₁ given in equation (4b), the corresponding CB₂ is given belowwhere e_(n) denotes a length-8 column vector with 1 in the n-th row andzero elements elsewhere:{[e₁ e₃],[e₁ e₅],[e₁ e₇], [e₂ e₄], [e₂ e₆],[e₂ e₈],[e₃ e₅],[e₃ e₇],[e₄e₆],[e₄ e₈],[e₅ e₇],[e₆ e₈]}The composite rank-2 codebook is then computed as W=W₁W₂.

Table 2 is a beam angle table of the resulting orthogonal vectors basedon equation (4b).

TABLE 2 θ (beam Set of θ's resulting in orthogonal n angle) vectorswithin the same W₁ 0 0 {π/4, π/2, 3π/4}  π/8 π/8 + {π/4, π/2, 3π/4}  π/4{0, π/2, 3π/4} 3π/8 π/8 + {0, π/2, 3π/4}  π/2 {0, π/4, 3π/4} 5π/8 π/8 +{0, π/4, 3π/4} 3π/4 {0, π/4, π/2} 7π/8 π/8 + {0, π/4, π/2} 1 π π + {π/4,π/2, 3π/4} 9π/8 9π/8 + {π/4, π/2, 3π/4} 5π/4 π + {0, π/2, 3π/4} 11π/8 9π/8 + {0, π/2, 3π/4} 4π/3 π + {0, π/4, 3π/4} 13π/8  9π/8 + {0, π/4,3π/4} 7π/4 π + {0, π/4, π/2} 15π/8  9π/8 + {0, π/4, π/2}Rank-3 and rank-4 codebooks can be designed similarly. Following theabove design methodology:

A size-8 rank-3 codebook (and hence CB₂) can be constructed for a givenW₁ (or n). Here, CB₂ is:

{[e₁ e₃ e₅],[e₁ e₃ e₇],[e₁ e₅ e₇],[e₃ e₅ e₇],[e₂ e₄ e₆], [e₂ e₄ e₈],[e₂e₆ e₈],[e₄ e₆ e₈]}

A size-2 rank-4 codebook (and hence CB₂) can be constructed for a givenW₁ or n.

-   -   {[e₁ e₃ e₅ e₇],[e₂ e₄ e₆ e₈]}

In the second part of this invention, a dual-codebook design exploits acertain product structure of the spatial channel. This is suitable forpairs of ULA as well as pairs of dual-polarized array setup asillustrated in FIG. 4. Using the 8 Tx dual-polarized setup illustratedin FIG. 4(b) and assuming the spacing of L/2 between two dual-polarizedantenna elements, the spatial channel covariance matrix can beapproximated as follows:

${C \approx \begin{bmatrix}C_{H} & 0 \\0 & C_{V}\end{bmatrix}} = \begin{bmatrix}C_{{ULA} - 4} & 0 \\0 & C_{{ULA} - 4}\end{bmatrix}$The 4×4 covariance matrices C_(H) and C_(V) follow that of the 4 Tx ULA.The spatial covariance matrix is block diagonal since the spatialchannel coefficients associated with different polarizations areuncorrelated. Thus even with L/2 spacing, a rank-2 transmission canoccur quite often. Two different structures are possible. In the firststructure the elements associated with different polarization groups arecombined via the second stage precoding where Y collapses the twopolarization groups into one.

$\begin{matrix}{W = {\begin{bmatrix}{\alpha_{H}{XY}} \\{\alpha_{V}{XY}}\end{bmatrix} = {{\begin{bmatrix}\alpha_{H} \\\alpha_{V}\end{bmatrix} \otimes ({XY})} = {{\alpha \otimes ({XY})} = {{\begin{bmatrix}X & 0 \\0 & X\end{bmatrix}\left( {\alpha \otimes Y} \right)} = {W_{1}W_{2}}}}}}} & (6)\end{matrix}$This scheme does not allow transmission higher than rank-4. In fact arank>1 will not occur frequently with L/2 spacing. Thus equation (6) ismore suitable for rank-1 transmission in this particular antenna setup.While this scheme may increase precoding diversity gain, the twodifferent polarization groups should also be used spatial multiplexingdue to the uncorrelated nature of the different polarization groups. Totake advantage of such property, equation (6) can be expanded asfollows:

$\begin{matrix}{W = {{\begin{bmatrix}X & 0 \\0 & X\end{bmatrix}\begin{bmatrix}{\alpha_{HH}Y_{1}} & {\alpha_{HV}Y_{2}} \\{\alpha_{VH}Y_{1}} & {\alpha_{VV}Y_{2}}\end{bmatrix}} = {W_{1}W_{2}}}} & (7)\end{matrix}$Equation (7) is reduced to equation (6) when α_(HV) and α_(VV) are setto zero. Y₁ and Y₂ can be the same or different. For this particularantenna setup, the matrix X can be constructed based on the oversampled4 Tx DFT vectors. Analogous to the first embodiment, any oversamplingfactor can be used such as 4× oversampling or 8× oversampling. For theshort-term and/or frequency selective component W₂ typical co-phasingcoefficients can be used for (α_(H), α_(V)) or (α_(HM), α_(VH)α_(HV),α_(VV)). The coefficients belong to QPSK or 8PSK alphabet. Thus α_(H)=1and

$\alpha_{V} = e^{j*2\pi\frac{k}{N}}$where k=0, 1 . . . N−1 with an appropriate normalization. The matrix Yor Y₁/Y₂ represent selection or group selection of the columns of X.

The design in the second invention can also be used for 8 Tx ULA arraysince the block-diagonal design constructed from two 4 Tx DFT matricescan be used to generate all the 8 Tx DFT beam angles with appropriateco-phasing operation in W₂. This property holds due to the so-calledbutterfly property of DFT operations.

An exemplary first embodiment uses the 4× oversampled 4 Tx DFT vectorsat generate 4 beam angles per polarization group. The beam angle spaceis partitioned into 4 non-overlapping groups resulting in W₁ of size 8×8block diagonal matrix since X is a 4×4 matrix:

$\begin{matrix}{{{X^{(n)} = {\frac{1}{2} \times {\begin{bmatrix}1 & 0 & 0 & 0 \\0 & (j)^{n} & 0 & 0 \\0 & 0 & \left( {- 1} \right)^{n} & 0 \\0 & 0 & 0 & \left( {- j} \right)^{n}\end{bmatrix}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & e^{j\frac{\pi}{8}} & e^{{j{(2)}}\frac{\pi}{8}} & e^{{j{(3)}}\frac{\pi}{8}} \\1 & e^{{j{(2)}}\frac{\pi}{8}} & e^{{j{(2)}}{(2)}\frac{\pi}{8}} & e^{{j{(2)}}{(3)}\frac{\pi}{8}} \\1 & e^{{j{(3)}}\frac{\pi}{8}} & e^{{j{(2)}}{(3)}\frac{\pi}{8}} & e^{{j{(3)}}{(3)}\frac{\pi}{8}}\end{bmatrix}}}},\mspace{20mu}{n = 0},1,2,3}\mspace{20mu}{{W_{1}^{(n)} = \begin{bmatrix}X^{(n)} & 0 \\0 & X^{(n)}\end{bmatrix}},{{CB}_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},W_{1}^{(3)}} \right\}}}} & (8)\end{matrix}$With the above choice of X, the following size-16 W₂ codebook design canbe used for rank-1 transmission. Here QPSK co-phasing is used.

$\begin{matrix}{{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{j\; Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- j}\; Y}\end{bmatrix}}} \right\}}\mspace{20mu}{Y \in \left\{ {\begin{bmatrix}1 \\0 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\1 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\1 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\0 \\1\end{bmatrix}} \right\}}} & (9)\end{matrix}$For rank-2 transmission, the following W₂ codebook design can be used.This is also based on the QPSK alphabet and Y₁=Y₂=Y. In general Y₁ andY₂ can be different.

$\begin{matrix}{{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\Y & {- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\{j\; Y} & {{- j}\; Y}\end{bmatrix}}} \right\}}{Y \in \left\{ {\begin{bmatrix}1 \\0 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\1 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\1 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\0 \\1\end{bmatrix}} \right\}}} & (10)\end{matrix}$The first exemplary embodiment uses 16 4 Tx oversampled DFT beam anglesfor constructing X and partitions them into 4 non-overlapping groups.This results in 4 W₁ matrices. Alternatively, each X may be constructedwith the same size 4×4 matrix which represents more than 4 overlappinggroups of beam angles. Thus for each X two adjacent X matrices willoverlap in 2 beam angles. This is motivated to reduce the so-called edgeeffect in the precoder selection since W₁ is typically chosen before W₂.This is relevant only for frequency-selective precoding where differentprecoders W=W₁*W₂ can be used for different parts of the transmissionbandwidth such as sub-bands.

Based this design philosophy, a second exemplary embodiment is describedin equation (11) with appropriate scalar normalization.

$\begin{matrix}{\mspace{85mu}{{{{B = \begin{bmatrix}b_{0} & b_{1} & \ldots & b_{N\; - \; 1}\end{bmatrix}},{\lbrack B\rbrack_{{l + m},\;{l + n}}\; = \;{e\;}^{j\frac{2\pi\;{mn}}{N}}}}\mspace{20mu}{{m = 0},1,2,3}\mspace{31mu}\mspace{20mu}{{n = 0},1,\ldots\mspace{14mu},{N - 1}}{X^{(k)} \in \left\{ {{{\left\lbrack {b_{{({N_{b}{k/2}})}{mod}\; N}\mspace{14mu} b_{{({{N_{b}{k/2}} + 1})}{mod}\; N}\mspace{14mu}\ldots\mspace{14mu} b_{{({{N_{b}{k/2}} + N_{b} - 1})}{mod}\; N}} \right\rbrack:k} = 0},1,\ldots\mspace{14mu},{\frac{2\; N}{N_{b}} - 1}} \right\}}}\mspace{20mu}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},\mspace{20mu}{C_{1}\; = \;\left\{ {W_{1}^{(0)},\; W_{1}^{(1)},\; W_{1}^{(2)},\;\ldots\mspace{14mu},\; W_{1}^{{({2\;{N/N_{b}}})}\; - \; 1}} \right\}}}}} & (11)\end{matrix}$where: W₁ is a block diagonal matrix of X; X is a 4×Nb matrix; and Nbdenotes the number of adjacent 4 Tx DFT beams contained in X. Such adesign is able to synthesize N 4 Tx DFT beams within each polarizationgroup. For a given N, the spatial oversampling factor is essentiallyN/4. The overall 4 Tx DFT beam collections are captured in the 4×Nmatrix B. Using co-phasing in W₂ the composite precoder W can synthesizeup to N 8 Tx DFT beams. Allowing an overlapping of Nb/2 beam anglesbetween two consecutively-indexed W₁ matrices, the set of W₁ matricesrepresents (2N/Nb)-level partitioning of the N 4 Tx beam angles in X,each polarization group. This design results in a codebook size of 2N/Nbfor W₁. The construction of W₂ codebook can be performed accordingly.

Based on the overlapping design given in equation (11), some exemplaryconstructions for W₂ codebook are given below. To construct at least 168 Tx DFT beam angles, N=16 is chosen. As the choice of W₁ codebook canbe different for different transmission ranks, one W₁ codebook design ischosen for ranks 1 and 2, and another W₁ codebook design chosen forranks 3 and 4. For ranks 1 and 2, Nb=4 allows good trade-off betweenfrequency-selective precoding gain and feedback overhead. For ranks 3and 4, Nb=8 accommodates higher-rank transmission which tends to undergochannels with richer scattering. The complete design for ranks 1, 2, 3,and 4 are given below. For rank-5 to 8, 8 Tx precoding tends to belimited for practical antenna setups. Thus the design for rank-5 to 8 isnot given thus fixed precoding can be used. The examples below use thefollowing notations: (1) {tilde over (e)}_(M) is a 4×1 selection vectorwith all zeros except for the n-th element with value 1; (2) e_(n) is a8×1 selection vector with all zeros except for the n-th element withvalue 1. The W₂ matrix chooses a column vector or a group of columnvectors from the W₁ matrix for each polarization group where each groupis represented by one of the two block diagonal components whileperforming some co-phasing operation across the two polarization groups.

Rank-1:

$\mspace{20mu}{{B = \begin{bmatrix}b_{0} & b_{1} & \ldots & b_{15}\end{bmatrix}},{\lbrack B\rbrack_{{1 + m},{1 + n}} = e^{j\frac{{2\pi\;{mn}}\;}{16}}},\mspace{20mu}{m = 0},1,2,{{3\mspace{14mu} n} = 0},1,\ldots\mspace{14mu},15}$$X^{(k)} \in \left\{ {{{\begin{bmatrix}b_{{({2\; k})}{mod}\; 16} & b_{{({{2\; k} + 1})}{mod}\; 16} & b_{{({{2\; k} + 2})}{mod}\; 16} & b_{{({{2\; k} + 3})}{mod}\; 16}\end{bmatrix}\text{:}\mspace{14mu} k} = 0},1,\ldots\mspace{14mu},7} \right\}$$\mspace{20mu}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},\ldots\mspace{14mu},W_{1}^{(7)}} \right\}}}$$\mspace{20mu}{{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{j\; Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- j}\; Y}\end{bmatrix}}} \right\}},\mspace{20mu}{Y \in \left\{ {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{3},{\overset{\sim}{e}}_{4}} \right\}}}$Rank-2:The W₁ codebook design is the same as rank-1.

$\mspace{20mu}{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{j\; Y_{1}} & {{- j}\; Y_{2}}\end{bmatrix}}} \right\}}$$\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{1}} \right),\left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{2}} \right),\left( {{\overset{\sim}{e}}_{3},{\overset{\sim}{e}}_{3}} \right),\left( {{\overset{\sim}{e}}_{4},{\overset{\sim}{e}}_{4}} \right),\left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{2}} \right),\left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{3}} \right),\left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{4}} \right),\left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{4}} \right)} \right\}$Rank-3:

$\mspace{20mu}{{B = \begin{bmatrix}b_{0} & b_{1} & \ldots & b_{15}\end{bmatrix}},{\lbrack B\rbrack_{{1 + m},{1 + n}} = e^{j\frac{2\pi\;{mn}}{16}}},\mspace{20mu}{m = 0},1,2,{{3\mspace{14mu} n} = 0},1,\ldots\mspace{14mu},15}$$X^{(k)} \in \left\{ {{{\begin{bmatrix}b_{{({4\; k})}{mod}\; 16} & b_{{({{4\; k} + 1})}{mod}\; 16} & \ldots & b_{{({{4\; k} + 7})}{mod}\; 16}\end{bmatrix}\text{:}\mspace{14mu} k} = 0},1,2,3} \right\}$$\mspace{20mu}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},W_{1}^{(3)}} \right\}}}$$\mspace{20mu}{{W_{2} \in {CB}_{2}} = \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}} \right\}}$$\left( {Y_{1},Y_{2}} \right) \in \begin{Bmatrix}{\left( {e_{1},\left\lbrack {e_{1}\mspace{14mu} e_{5}} \right\rbrack} \right),} & {\left( {e_{2},\left\lbrack {e_{2}\mspace{14mu} e_{6}} \right\rbrack} \right),} & {\left( {e_{3},\left\lbrack {e_{3}\mspace{14mu} e_{7}} \right\rbrack} \right),} & {\left( {e_{4},\left\lbrack {e_{4}\mspace{14mu} e_{8}} \right\rbrack} \right),} \\{\left( {e_{5},\left\lbrack {e_{1}\mspace{14mu} e_{5}} \right\rbrack} \right),} & {\left( {e_{6},\left\lbrack {e_{2}\mspace{14mu} e_{6}} \right\rbrack} \right),} & {\left( {e_{7},\left\lbrack {e_{3}\mspace{14mu} e_{7}} \right\rbrack} \right),} & {\left( {e_{8},\left\lbrack {e_{4}\mspace{14mu} e_{8}} \right\rbrack} \right),} \\{\left( {\left\lbrack {e_{1}\mspace{14mu} e_{5}} \right\rbrack,e_{5}} \right),} & {\left( {\left\lbrack {e_{2}\mspace{14mu} e_{6}} \right\rbrack,e_{6}} \right),} & {\left( {\left\lbrack {e_{3}\mspace{14mu} e_{7}} \right\rbrack,e_{7}} \right),} & {\left( {\left\lbrack {e_{4}\mspace{14mu} e_{8}} \right\rbrack,e_{8}} \right),} \\{\left( {\left\lbrack {e_{5}\mspace{14mu} e_{1}} \right\rbrack,e_{1}} \right),} & {\left( {\left\lbrack {e_{6}\mspace{14mu} e_{2}} \right\rbrack,e_{2}} \right),} & {\left( {\left\lbrack {e_{7}\mspace{14mu} e_{3}} \right\rbrack,e_{3}} \right),} & \left( {\left\lbrack {e_{8}\mspace{14mu} e_{4}} \right\rbrack,e_{4}} \right)\end{Bmatrix}$Rank-4:The W₁ codebook design is the same as rank-3.

${W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\Y & {- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\{j\; Y} & {{- j}\; Y}\end{bmatrix}}} \right\}$ $Y \in \left\{ {\begin{bmatrix}e_{1} & e_{5}\end{bmatrix},\begin{bmatrix}e_{2} & e_{6}\end{bmatrix},\begin{bmatrix}e_{3} & e_{7}\end{bmatrix},\begin{bmatrix}e_{4} & e_{8}\end{bmatrix}} \right\}$

Other exemplary constructions, variations, and embodiments can bedesigned based on these principles. These two designs are not exclusiveof each other. It is possible to combine designs 1 and 2 into onecodebook framework as depicted in FIG. 3. The different W₁ matricescorresponding to different designs are enumerated with PMI₁ while thecodebook CB₂ for W₂ is dependent on the choice of W₁. Such a setupallows the 8 Tx design to accommodate for several scenarios including 8Tx ULA and pairs of dual-polarized elements. It is also possible toinclude other designs for W₁ such as a Grassmanian codebook or virtualantenna selection components which are suitable for low spatialcorrelation. The W₂ codebook can be different for different W₁ matrices.While the codebook example is presented covering a multi-rank format ofrank-1 to rank-4, any multi-rank design constructed from taking at leastone rank-specific codebook(s) from one example and some otherrank-specific codebook(s) from other example(s) is not precluded. Amulti-rank codebook may be constructed from a subset of a design. It ispossible to construct a multi-rank codebook which uses the rank-1 andrank-2 designs from any of the examples below but which uses a fixedmatrix precoding “size-1 codebook” for rank-3 and above.

Some UE feedback signaling mechanisms to support the dual-codebookdesigns given above in the context of 3GPP LTE-Advanced systems. In LTERel. 8 and 9, there are currently two UE feedback mechanisms for PHIreporting: (1) Periodic reporting on Physical Uplink Control CHannel(PUCCH) with the content possibly piggybacked onto Physical UplinkShared CHannel (PUSCH) in the presence of uplink (UL) grant withwideband frequency non-selective PMI; and (2) Aperiodic reporting onPUSCH which allows frequency-selective PMI reporting. For LTE-A, somenew reporting schemes may be introduced such as periodic PUSCH and newformats on PUCCH and PUSCH based reports. A UE may transmit on bothPUCCH and PUSCH at the same time. This patent application focuses on howthe two-stage PHI is periodically reported on PUCCH. Reporting PMI₁long-term PMI can be treated analogous to rank indicator (RI) where thereporting interval for RI can be configured larger than channel qualityindicator/precoding matrix indicator (CQI/PMI) for PUCCH basedreporting. Thus the reporting mechanism for the long-term PMI₁ can bedesigned as follows:

(1) The reporting instances subframes of PMI₁ are aligned (identical)with those of RI. PMI₁ is reported in the same subframes as RI. This isa reasonable solution to avoid complication due to inter-dependenceamong reports. The following possibilities exist: PMI₁ is reported atthe same periodicity as RI; and PMI₁ is reported at larger periodicitythan RI where the periodicity of PMI₁ is an integer Q multiple of thatof RI (Q=1, 2, 3 . . . ). The first possibility is a special case of thesecond where the integer multiple is 1.

(2) While it is possible to reserve a different PUCCH resource forreporting PMI₁, this seems unnecessary since the PUCCH resource used forreporting RI which is at most 3 bits for 8 Tx can still accommodate afew more bits as long as the payload size of PMI₁ is not excessive. ThusPMI₁ is not only reported at the same subframes as RI, but also sharesthe same PUCCH resource as RI. PMI₂ is then treated as the Rel. 8/9 LTEPMI which is reported together with CQI.

FIG. 5 illustrates an example where the reporting periodicity of RI/PMI₁is 4× as that of wideband CQI/PMI₂ with reporting offset of zero wherePMI₁ has the same periodicity as the RI. Subframes 501 and 505 reportboth RI and PMI₁. Subframes 502, 503, 504, 506, 507 and 508 reportwideband CQI and PMI₂. Thus the periodicity of RI/PMI₁ is 4× as that ofwideband CQI/PMI₂.

As an alternative, the reporting periodicity subframes of PMI₁ can besmaller than that of RI. There are several possibilities. In oneembodiment, PMI₁ is reported with the same periodicity as PMI₂. In thiscase PMI₁ and PMI₂ possess the same time-domain granularity are alwaysreported together. The RI reporting periodicity is O times that of thePMI₁/PMI₂ reporting periodicity where O is a positive integer. Thefrequency-domain granularity of PMI₁ and PMI₂ may be different. PMI₁ maybe a wideband precoder while PMI₂ may be either wideband or subband.FIG. 6 illustrates an example of this periodicity. Subframes 601 and 604report RI. Subframes 602, 603, 605 and 606 report PMI₁, PMI₂ and CQI.

In another embodiment, PMI₁ is reported at larger perodicity than PMI₂and RI is reported at larger periodicity than PMI₁. For example, RIreporting periodicity is 01 times that of reporting periodicity of PMI₁and PMI₁ periodicity is O2 times that of PMI₂. This is illustrated inFIG. 7. Subframes 701 and 708 report RI. Subframes 702, 705, 709 and 712report PMI₁. Subframes 703, 704, 706, 707, 710, 711, 713 and 714 reportPMI₂ and CQI. This is perhaps the least desirable mode of operationdespite its apparent flexibility.

The description of this invention has focused on the design of codebooksand its associated signaling for 8-antenna (8 Tx) systems. Thosefamiliar with the art would understand that this invention can beextended to different number of transmit antennas at the eNodeB. Anextension for 4 Tx systems in the context of 3GPP LTE is as follows.3GPP LTE Release 8 (Rel. 8) supports a codebook-based precoding andfeedback for 4 Tx systems. Using the dual-codebook product designW=W₁W₂, it is possible to augment the Release 8 design for performanceimprovement with lower rank transmissions such as rank-1 and/or rank-2.This can benefit MU-MIMO operation. One possible embodiment uses theRel. 8 4 Tx codebook for the short-term precoding component W₂. W₁ isthen defined to achieve the design goal. This permits the designer toadd more W₁ matrices to cater for spatial channel scenarios such asantenna setup, angular spread, etc.

One embodiment improves rank-1 transmission MU-MIMO performance for the4 Tx ULA setup with L/2 spacing. The Rel. 8 4 Tx codebook includes 8 4Tx and hence 2× oversampling DFT vectors, additional DFT vectors allowhigher spatial resolution using 16 4 Tx DFT vectors including those fromthe Rel. 8 codebook. If the DFT vectors from the Rel. 8 codebook areused, a possible embodiment is:

(1) For a given value of n spatial/angular oversampling factor, ncontiguous groups are defined.

(2) The size of each contiguous group is 4. Each contiguous group isassociated with one W₁ matrix. For the i-th group (i=0, 1, . . . , n−1):

$\begin{matrix}{W_{1}^{(i)} = {{\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & j & {- 1} & {- j} \\1 & {- 1} & 1 & {- 1} \\1 & {- j} & {- 1} & j\end{bmatrix}}^{H}\left( {{\frac{1}{2} \times \begin{bmatrix}1 & 0 & 0 & 0 \\0 & e^{{j{(4)}}\frac{\pi}{2\; n}{\mathbb{i}}} & 0 & 0 \\0 & 0 & e^{{j{(2)}}{(4)}\frac{\pi}{2\; n}{\mathbb{i}}} & 0 \\0 & 0 & 0 & e^{{j{(3)}}{(4)}\frac{\pi}{2\; n}{\mathbb{i}}}\end{bmatrix}\left. \quad\begin{bmatrix}1 & 1 & 1 & 1 \\1 & e^{j\frac{\pi}{2\; n}} & e^{{j{(2)}}\frac{\pi}{2\; n}} & e^{{j{(3)}}\frac{\pi}{2\; n}} \\1 & e^{{j{(2)}}\frac{\pi}{2\; n}} & e^{{j{(2)}}{(2)}\frac{\pi}{2\; n}} & e^{{j{(2)}}{(3)}\frac{\pi}{2\; n}} \\1 & e^{{j{(3)}}\frac{\pi}{2\; n}} & e^{{j{(2)}}{(3)}\frac{\pi}{2\; n}} & e^{{j{(3)}}{(3)}\frac{\pi}{2\; n}}\end{bmatrix} \right)} = {{{\frac{1}{4}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & {- j} & {- 1} & j \\1 & {- 1} & 1 & {- 1} \\1 & j & {- 1} & {- j}\end{bmatrix}}\begin{bmatrix}1 & 0 & 0 & 0 \\0 & e^{{j{(4)}}\frac{\pi}{2\; n}{\mathbb{i}}} & 0 & 0 \\0 & 0 & e^{{j{(2)}}{(4)}\frac{\pi}{2\; n}{\mathbb{i}}} & 0 \\0 & 0 & 0 & e^{{j{(3)}}{(4)}\frac{\pi}{2\; n}{\mathbb{i}}}\end{bmatrix}}{\quad\begin{bmatrix}1 & 1 & 1 & 1 \\1 & e^{j\frac{\pi}{2\; n}} & e^{{j{(2)}}\frac{\pi}{2\; n}} & e^{{j{(3)}}\frac{\pi}{2\; n}} \\1 & e^{{j{(2)}}\frac{\pi}{2\; n}} & e^{{j{(2)}}{(2)}\frac{\pi}{2\; n}} & e^{{j{(2)}}{(3)}\frac{\pi}{2\; n}} \\1 & e^{{j{(3)}}\frac{\pi}{2\; n}} & e^{{j{(2)}}{(3)}\frac{\pi}{2\; n}} & e^{{j{(3)}}{(3)}\frac{\pi}{2\; n}}\end{bmatrix}}}} \right.}} & (12)\end{matrix}$Only the first 4 DFT vectors in equation (12) are used for CB₂ for v=1codebook. That is:

$\begin{matrix}{{{CB}_{2} = {\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & j & {- 1} & {- j} \\1 & {- 1} & 1 & {- 1} \\1 & {- j} & {- 1} & j\end{bmatrix}}}\left( {{in}\mspace{14mu}{the}\mspace{14mu}{form}\mspace{14mu}{of}\mspace{14mu} 4 \times 4\mspace{14mu}{matrix}} \right)} & (13)\end{matrix}$Note that in equation (12) the 4-DFT matrix forms a complete orthonormalbasis for 4-dimensional complex vector space. For n=4, this designresults in 4 contiguous groups (which results in a 2-bit PMI₁ per PMIreport) and 2-bit PMI₂ for rank-1 for v=1.

To allow a natural dynamic switching with SU-MIMO applications where theother 8 vectors in the v=1 codebook may be more useful, this codebookcan augment the Rel. 8 4 Tx codebook. For the original Rel. 8 codebook,W₁ is chosen to be an identity matrix where CB₂ is simply the Rel. 8codebook. This allows dynamic switching between the two W₁ matrices viaan update of PMI₁. When PMI₁ indicates that W₁ identity is chosen, CB₂is chosen as the original Rel. 8 codebook. When PMI₁ indicates someother W₁, W₁ and CB₂ are chosen as the enhanced component given above.

Another embodiment is applicable for rank-1 or rank-2 transmissionsaimed at improving MU-MIMO performance for the 4 Tx dual-polarizedantenna setup. The enhanced component can be designed independently ofthe Rel. 8 codebook. The enhanced component can be combined with theRel. 8 codebook via the same augmentation procedure of choosing W₁. Thatis:

(1) When PMI₁ indicates that W₁ identity is chosen, CB₂ is chosen as theoriginal Rel. 8 codebook.

(2) When PMI_(Z) indicates some other W₁, W₁ and CB₂ are chosen as theenhanced component.

For the enhanced components not including when W₁ is the identity matrixand CB₂ is the Rel. 8 codebook, a design similar to the 8 Tx counterpartcan be used. For example, a Nb/2 overlapping beam design is used for W₁.This can be written as follows.

$\begin{matrix}{\mspace{79mu}{{{B = \begin{bmatrix}b_{0} & b_{1} & \ldots & b_{N - 1}\end{bmatrix}},{\lbrack B\rbrack_{{1 + m},{1 + n}} = {\frac{1}{\sqrt{2}}e^{j\frac{2\pi\;{mn}}{N}}}},\mspace{20mu}{m = 0},{{1\mspace{25mu} n} = 0},1,\ldots\mspace{14mu},{N - 1}}{X^{(k)} \in \begin{Bmatrix}{\begin{bmatrix}b_{{({N_{b}{k/2}})}{mod}\; N} & b_{{({{N_{b}{k/2}} + 1})}{mod}\; N} & \ldots & b_{{({{N_{b}{k/2}} + N_{b} - 1})}{mod}\; N}\end{bmatrix}\text{:}} \\{{k = 0},1,\ldots\mspace{14mu},{\frac{2\; N}{N_{b}} - 1}}\end{Bmatrix}}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},\ldots\mspace{14mu},W_{1}^{{({2\;{N/N_{b}}})} - 1}} \right\}}}}} & (14)\end{matrix}$The same W₂ design as that for the 8 Tx case can be applied for a givenvalue of N and Nb. The following design concept for W₂ can be used forthe enhanced components.

(1) The first part of W₂ utilizes beam selection or beam group selectionwithin each polarization group. The same or different beam(s) can beused for different polarization groups.

(2) The second part of W₂ utilizes co-phasing between two differentpolarization groups. The co-phasing can be done with a unitary vector ormatrix assuming a certain alphabet size such as QPSK or 8PSK.

The combination of beam selection and co-phasing in W₂ combined with W₁should result in a unitary precoder W=W₁*W₂.

Assuming the same beam (group) selection for different polarizationgroups and QPSK-based co-phasing, the following W₂ design can be usedfor:

Nb=2:

Rank-1

${{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{j\; Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- j}\; Y}\end{bmatrix}}} \right\}},{Y \in \left\{ {\begin{bmatrix}1 \\0\end{bmatrix},\begin{bmatrix}0 \\1\end{bmatrix}} \right\}}$Rank-2:

${{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\Y & {- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\{j\; Y} & {{- j}\; Y}\end{bmatrix}}} \right\}},{Y \in \left\{ {\begin{bmatrix}1 \\0\end{bmatrix},\begin{bmatrix}0 \\1\end{bmatrix}} \right\}}$Nb=4:Rank-1:

${{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{j\; Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- j}\; Y}\end{bmatrix}}} \right\}},{Y \in \left\{ {\begin{bmatrix}1 \\0 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\1 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\1 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\0 \\1\end{bmatrix}} \right\}}$Rank-2:

${{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\Y & {- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\{j\; Y} & {{- j}\; Y}\end{bmatrix}}} \right\}},{Y \in \left\{ {\begin{bmatrix}1 \\0 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\1 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\1 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\0 \\1\end{bmatrix}} \right\}}$Nb=8:Here, e_(n) denotes an 8×1 selection vector with all zeros except forthe n-th element with value 1.Rank-1:

${{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{j\; Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- j}\; Y}\end{bmatrix}}} \right\}},{Y \in \left\{ {e_{1},e_{2},e_{3},\ldots\mspace{14mu},e_{8}} \right\}}$Rank-2:

${{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\Y & {- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\{j\; Y} & {{- j}\; Y}\end{bmatrix}}} \right\}},{Y \in \left\{ {e_{1},e_{2},e_{3},\ldots\mspace{14mu},e_{8}} \right\}}$For the rank-1 design, co-phasing with larger alphabet size can also bedone. Although less advantageous this design can be expressed as followsassuming L-PSK co-phasing:

${W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{e^{j\frac{2\pi}{L}l}Y}\end{bmatrix}},{l = 0},1,\ldots\mspace{14mu},{L - 1}} \right\}$For the rank-2 design it is possible to select two different beam anglesinstead of one. This design may be beneficial for ULA scenarios. Therank-2 design for W₂ can be described in the following more genericformulation assuming QPSK-based co-phasing:

$\begin{matrix}{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{j\; Y_{1}} & {{- j}\; Y_{2}}\end{bmatrix}}} \right\}} & (15)\end{matrix}$Notice that equation (15) is reduced to the previous examples whenY₁=Y₂=Y. If Y₁ is not equal to Y₂, then vectors Y₁ and Y₂ should becarefully chosen so that the resulting composite rank-2 precoder isunitary. This may not be possible for all combinations of N and Nb suchas Nb<N/2.

With respect to the enhanced components, while the codebook example ispresented covering multi-rank format such as rank-1 to rank-2, anymulti-rank design constructed from taking at least one rank-specificcodebook(s) from one example and some other rank-specific codebook(s)from other example(s) is possible. It is also possible to construct amulti-rank codebook from a subset of a design. A multi-rank codebookwhich uses the rank-1 design may be constructed from any of the examplesbelow, but use the rank-2 design from another example. It is desirableto keep the maximum overhead associated with W₂ PMI₂ payload the same asRel. 8. This implies that PMI₂ occupies no more than 4 bits. This mayrequire a subset of all the possible W₂ matrices needs to be used forsome cases to keep the size for CB₂ no more than 16. With Nb=8 rank-1,the possible total size of CB₂ is 32. To keep the size within 16, only16 out of 32 matrices are selected to form CB₂. It is also possible toselect an even smaller subset especially for rank-2. Since the maintarget of enhancement is MU-MIMO, it is possible not to use anyenhancement for rank-2. Thus only the above rank-1 design is augmentedwith the Rel. 8 codebook. Furthermore, since the enhanced component isan augmentation of the Rel. 8 codebook, it will be combined with theRel. 8 codebook based on the principle stated above. In this case, it ispossible to further prune the enhanced codebook component due toredundancy such as some of the vectors/matrices in the enhancedcomponent are identical to some of the vectors/matrices in the Rel. 8codebook. This occurs since Rel. 8 codebook already contains 8 4 Tx DFTvectors in its rank-1 design. This can further reduce the size of W₁and/or W₂ codebooks, or at least reduce the necessary PMI₁/PMI₂ payloadwhich could be beneficial in some scenarios such as PUCCH basedfeedback. Using a subset or entirety of the above codebook designexamples combined with some other designs is also within the scope ofthis invention which should be clear for those familiar with the art.

Two examples of complete design with augmentation are given below.

Example 1: Block Diagonal Overlapping GoB (N=8, Nb=4) Augmentation Onlyfor Rank 1

$\mspace{20mu}{{B = \begin{bmatrix}b_{0} & b_{1} & \ldots & b_{7}\end{bmatrix}},{\lbrack B\rbrack_{{1 + m},{1 + n}} = e^{j\frac{2\pi\;{mn}}{8}}},\mspace{20mu}{m = 0},{{1\mspace{25mu} n} = 0},1,\ldots\mspace{14mu},7}$$X^{(k)} \in \left\{ {{{\begin{bmatrix}b_{{({2\; k})}{mod}\; 8} & b_{{({{2\; k} + 1})}{mod}\; 8} & b_{{({{2\; k} + 2})}{mod}\; 8} & b_{{({{2\; k} + 3})}{mod}\; 8}\end{bmatrix}\text{:}\mspace{14mu} k} = 0},1,2,3} \right\}$Rank 1:

${W_{1} \in C_{1}} = \left\{ {I_{4},\begin{bmatrix}X^{(0)} & 0 \\0 & X^{(0)}\end{bmatrix},\begin{bmatrix}X^{(1)} & 0 \\0 & X^{(1)}\end{bmatrix},\begin{bmatrix}X^{(2)} & 0 \\0 & X^{(2)}\end{bmatrix},\begin{bmatrix}X^{(3)} & 0 \\0 & X^{(3)}\end{bmatrix}} \right\}$Size-5 is the Rel. 8 codebook augmented with block diagonal GoB.When W₁=I₄: W₂∈C_(2,R8Tx4r1), where C_(2,R8Tx4r1) denotes the Rel. 8 4Tx rank-1 codebook used for W₂.When

$\mspace{20mu}{W_{1} = {\begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}\mspace{14mu}\left( {{k = 0},1,2,3} \right)\text{:}}}$${{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{j\; Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- j}\; Y}\end{bmatrix}}} \right\}},\mspace{20mu}{Y \in \left\{ {\begin{bmatrix}1 \\0 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\1 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\1 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\0 \\1\end{bmatrix}} \right\}}$Rank 2:W₁=I₄ is the size-1 Rel. 8 codebook only.W₂∈C_(2,R8Tx4r2), where C_(2,R8Tx4r2) denotes the Rel. 8 4 Tx rank-2codebook used for W₂.Rank 3:W₁=I₄ is the size-1 Rel. 8 codebook only.W₂∈C_(2,R8Tx4r3), where C_(2,R8Tx4r3) denotes the Rel. 8 4 Tx rank-3codebook used for W₂.Rank 4:W₁=I₄ is the size-1 Rel. 8 codebook only.W₂∈C_(2,R8Tx4r4), where C_(2,R8Tx4r4) denotes the Rel. 8 4 Tx rank-4codebook used for W₂.

Example 2: Block Diagonal Non-Overlapping GoB (N=16, Nb=4) AugmentationOnly for Rank 1

$\mspace{20mu}{{B = \begin{bmatrix}b_{0} & b_{1} & \ldots & b_{15}\end{bmatrix}},{\lbrack B\rbrack_{{1 + m},{1 + n}} = e^{j\frac{{2\pi\;{mn}}\;}{16}}},\mspace{20mu}{m = 0},{{1\mspace{31mu} n} = 0},1,\ldots\mspace{14mu},15}$$X^{(k)} \in \left\{ {{{\begin{bmatrix}b_{{({4\; k})}{mod}\; 16} & b_{{({{4\; k} + 1})}{mod}\; 16} & b_{{({{4\; k} + 2})}{mod}\; 16} & b_{{({{4\; k} + 3})}{mod}\; 16}\end{bmatrix}\text{:}\mspace{14mu} k} = 0},1,2,3} \right\}$Rank 1:

${W_{1} \in C_{1}} = \left\{ {I_{4},\begin{bmatrix}X^{(0)} & 0 \\0 & X^{(0)}\end{bmatrix},\begin{bmatrix}X^{(1)} & 0 \\0 & X^{(1)}\end{bmatrix},\begin{bmatrix}X^{(2)} & 0 \\0 & X^{(2)}\end{bmatrix},\begin{bmatrix}X^{(3)} & 0 \\0 & X^{(3)}\end{bmatrix}} \right\}$is the size-5 Rel. 8 codebook augmented with block diagonal GoB.When W₁=I₄: W₂∈C_(2,R8Tx4r1), where C_(2,R8Tx4r1) denotes the Rel. 8 4Tx rank-1 codebook used for W₂.When

$\mspace{20mu}{W_{1} = {\begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}\mspace{14mu}\left( {{k = 0},1,2,3} \right)\text{:}}}$${{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{j\; Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- j}\; Y}\end{bmatrix}}} \right\}},\mspace{20mu}{Y \in \left\{ {\begin{bmatrix}1 \\0 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\1 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\1 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\0 \\1\end{bmatrix}} \right\}}$Rank 2:W₁=I₄ is the size-1 Rel. 8 codebook only.W₂∈C_(2,R8Tx4r2), where C_(2,R8Txr4r2) denotes the Rel. 8 4 Tx rank-2codebook used for W₂.Rank 3:W₁=I₄ is the size-1 Rel. 8 codebook only.W₂∈C_(2,R8Tx4r3), where C_(2,R8Tx4r3) denotes the Rel. 8 4 Tx rank-3codebook used for W₂.Rank 4:W₁=I₄ is the size-1 Rel. 8 codebook only.W₂∈C_(2,R8Tx4r4), where C_(2,R8Tx4r4) denotes the Rel. 8 4 Tx rank-4codebook used for W₂.

FIG. 8 is a block diagram illustrating internal details of an eNB 1002and a mobile UE 1001 in the network system of FIG. 1. Mobile UE 1001 mayrepresent any of a variety of devices such as a server, a desktopcomputer, a laptop computer, a cellular phone, a Personal DigitalAssistant (PDA), a smart phone or other electronic devices. In someembodiments, the electronic mobile UE 1001 communicates with eNB 1002based on a LTE or Evolved Universal Terrestrial Radio Access Network(E-UTRAN) protocol. Alternatively, another communication protocol nowknown or later developed can be used.

Mobile UE 1001 comprises a processor 1010 coupled to a memory 1012 and atransceiver 1020. The memory 1012 stores (software) applications 1014for execution by the processor 1010. The applications could comprise anyknown or future application useful for individuals or organizations.These applications could be categorized as operating systems (OS),device drivers, databases, multimedia tools, presentation tools,Internet browsers, emailers, Voice-Over-Internet Protocol (VOIP) tools,file browsers, firewalls, instant messaging, finance tools, games, wordprocessors or other categories. Regardless of the exact nature of theapplications, at least some of the applications may direct the mobile UE1001 to transmit UL signals to eNB (base-station) 1002 periodically orcontinuously via the transceiver 1020. In at least some embodiments, themobile UE 1001 identifies a Quality of Service (QoS) requirement whenrequesting an uplink resource from eNB 1002. In some cases, the QoSrequirement may be implicitly derived by eNB 1002 from the type oftraffic supported by the mobile UE 1001. As an example, VOIP and gamingapplications often involve low-latency uplink (UL) transmissions whileHigh Throughput (HTP)/Hypertext Transmission Protocol (HTTP) traffic caninvolve high-latency uplink transmissions.

Transceiver 1020 includes uplink logic which may be implemented byexecution of instructions that control the operation of the transceiver.Some of these instructions may be stored in memory 1012 and executedwhen needed by processor 1010. As would be understood by one of skill inthe art, the components of the uplink logic may involve the physical(PHY) layer and/or the Media Access Control (MAC) layer of thetransceiver 1020. Transceiver 1020 includes one or more receivers 1022and one or more transmitters 1024.

Processor 1010 may send or receive data to various input/output devices1026. A subscriber identity module (SIM) card stores and retrievesinformation used for making calls via the cellular system. A Bluetoothbaseband unit may be provided for wireless connection to a microphoneand headset for sending and receiving voice data. Processor 1010 maysend information to a display unit for interaction with a user of mobileUE 1001 during a call process. The display may also display picturesreceived from the network, from a local camera, or from other sourcessuch as a Universal Serial Bus (USB) connector. Processor 1010 may alsosend a video stream to the display that is received from various sourcessuch as the cellular network via RF transceiver 1020 or the camera.

During transmission and reception of voice data or other applicationdata, transmitter 1024 may be or become non-synchronized with itsserving eNB. In this case, it sends a random access signal. As part ofthis procedure, it determines a preferred size for the next datatransmission, referred to as a message, by using a power threshold valueprovided by the serving eNB, as described in more detail above. In thisembodiment, the message preferred size determination is embodied byexecuting instructions stored in memory 1012 by processor 1010. In otherembodiments, the message size determination may be embodied by aseparate processor/memory unit, by a hardwired state machine, or byother types of control logic, for example.

eNB 1002 comprises a Processor 1030 coupled to a memory 1032, symbolprocessing circuitry 1038, and a transceiver 1040 via backplane bus1036. The memory stores applications 1034 for execution by processor1030. The applications could comprise any known or future applicationuseful for managing wireless communications. At least some of theapplications 1034 may direct eNB 1002 to manage transmissions to or frommobile UE 1001.

Transceiver 1040 comprises an uplink Resource Manager, which enables eNB1002 to selectively allocate uplink Physical Uplink Shared CHannel(PUSCH) resources to mobile UE 1001. As would be understood by one ofskill in the art, the components of the uplink resource manager mayinvolve the physical (PHY) layer and/or the Media Access Control (MAC)layer of the transceiver 1040. Transceiver 1040 includes at least onereceiver 1042 for receiving transmissions from various UEs within rangeof eNB 1002 and at least one transmitter 1044 for transmitting data andcontrol information to the various UEs within range of eNB 1002.

The uplink resource manager executes instructions that control theoperation of transceiver 1040. Some of these instructions may be locatedin memory 1032 and executed when needed on processor 1030. The resourcemanager controls the transmission resources allocated to each UE 1001served by eNB 1002 and broadcasts control information via the PDCCH.

Symbol processing circuitry 1038 performs demodulation using knowntechniques. Random access signals are demodulated in symbol processingcircuitry 1038.

During transmission and reception of voice data or other applicationdata, receiver 1042 may receive a random access signal from a UE 1001.The random access signal is encoded to request a message size that ispreferred by UE 1001. UE 1001 determines the preferred message size byusing a message threshold provided by eNB 1002. In this embodiment, themessage threshold calculation is embodied by executing instructionsstored in memory 1032 by processor 1030. In other embodiments, thethreshold calculation may be embodied by a separate processor/memoryunit, by a hardwired state machine, or by other types of control logic,for example. Alternatively, in some networks the message threshold is afixed value that may be stored in memory 1032, for example. In responseto receiving the message size request, eNB 1002 schedules an appropriateset of resources and notifies UE 1001 with a resource grant.

What is claimed is:
 1. An apparatus for transmitting data in a wirelesscommunication system, comprising: circuitry for transmitting a precodingmatrix indicator (PMI) to a remote transceiver, wherein the PMIindicates a choice of a precoding matrix W derived from a matrixmultiplication of two matrices W1 and W2 from a first codebook C1 and asecond codebook C2, respectively, wherein the first codebook C1 includesat least the following matrices when the number of layers N is three orfour: $\mspace{20mu}{{B = \begin{bmatrix}b_{0} & b_{1} & \ldots & b_{15}\end{bmatrix}},{\lbrack B\rbrack_{{l + m},\;{l + n}}\; = e^{j\;\frac{{\;{2\;\pi\;{mn}}}\;}{16}}},\mspace{20mu}{m = 0},1,2,3}\mspace{31mu}$  n = 0, 1, …  , 15 $X^{(k)} \in \left\{ {{{\begin{bmatrix}b_{{({4\; k})}\;{mod}\; 16} & {b_{{({{4\; k} + 1})}\;{mod}\; 16}\mspace{14mu}\ldots} & b_{{({{4\; k} + 7})}\;{mod}\; 16}\end{bmatrix}:\; k} = 0},1,2,3} \right\}$$\mspace{20mu}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},W_{1}^{(3)}} \right\}},}$and wherein: the second codebook C2 includes at least the followingmatrices when the number of layers N is three and e_(n) is a 8×1selection vector with all zeros except for the n-th element with value1:$\mspace{20mu}{{W_{2}\; \in \;{CB}_{2}} = \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}} \right\}}$$\left( {Y_{1},\; Y_{2}} \right) \in {\begin{Bmatrix}{\left( {e_{1},\;\left\lbrack {e_{1}\mspace{25mu} e_{5}} \right\rbrack} \right),} & {\left( {e_{2},\;\left\lbrack {e_{2}\mspace{25mu} e_{6}} \right\rbrack} \right),} & {\left( {e_{3},\;\left\lbrack {e_{3}\mspace{25mu} e_{7}} \right\rbrack} \right),} & {\left( {e_{4},\;\left\lbrack {e_{4}\mspace{25mu} e_{8}} \right\rbrack} \right),} \\{\left( {e_{5},\;\left\lbrack {e_{1}\mspace{25mu} e_{5}} \right\rbrack} \right),} & {\left( {e_{6},\;\left\lbrack {e_{2}\mspace{25mu} e_{6}} \right\rbrack} \right),} & {\left( {e_{7},\;\left\lbrack {e_{3}\mspace{25mu} e_{7}} \right\rbrack} \right),} & {\left( {e_{8},\;\left\lbrack {e_{4}\mspace{25mu} e_{8}} \right\rbrack} \right),} \\{\left( {\left\lbrack {e_{1}\mspace{25mu} e_{5}} \right\rbrack,\; e_{5}} \right),} & {\left( {\left\lbrack {e_{2}\mspace{25mu} e_{6}} \right\rbrack,\; e_{6}} \right),} & {\left( {\left\lbrack {e_{3}\mspace{25mu} e_{7}} \right\rbrack,\; e_{7}} \right),} & {\left( {\left\lbrack {e_{4}\mspace{25mu} e_{8}} \right\rbrack,\; e_{8}} \right),} \\{\left( {\left\lbrack {e_{5}\mspace{25mu} e_{1}} \right\rbrack,\; e_{1}} \right),} & {\left( {\left\lbrack {e_{6}\mspace{25mu} e_{2}} \right\rbrack,\; e_{2}} \right),} & {\left( {\left\lbrack {e_{7}\mspace{25mu} e_{3}} \right\rbrack,\; e_{3}} \right),} & \left( {\left\lbrack {e_{8}\mspace{25mu} e_{4}} \right\rbrack,\; e_{4}} \right)\end{Bmatrix}.}$
 2. An apparatus for transmitting data in a wirelesscommunication system, comprising: circuitry for transmitting a precodingmatrix indicator (PMI) to a remote transceiver, wherein the PMIindicates a choice of a precoding matrix W derived from a matrixmultiplication of two matrices W1 and W2 from a first codebook C1 and asecond codebook C2, respectively, wherein the first codebook C1 includesat least the following matrices when the number of layers N is three orfour: $\mspace{20mu}{{B = \begin{bmatrix}b_{0} & b_{1} & \ldots & b_{15}\end{bmatrix}},{\lbrack B\rbrack_{{l + m},\;{l + n}}\; = \; e^{j\;\frac{{\;{2\;\pi\;{mn}}}\;}{16}}},\mspace{20mu}{m\; = \; 0},1,2,{{3\mspace{25mu} n}\; = \; 0},1,\ldots\mspace{14mu},15}$$X^{(k)} \in \left\{ {{{\begin{bmatrix}b_{{({4\; k})}\;{mod}\; 16} & b_{{({{4\; k} + 1})}\;{mod}\; 16} & \ldots & b_{{({{4\; k} + 7})}\;{mod}\; 16}\end{bmatrix}:\mspace{11mu} k}\; = \; 0},\; 1,\; 2,\; 3} \right\}$$\mspace{20mu}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1}\; = \;\left\{ {W_{1}^{(0)},\; W_{1}^{(1)},\; W_{1}^{(2)},\; W_{1}^{(3)}} \right\}},}$and wherein: the second codebook C2 includes at least the followingmatrices when the number of layers N is four and e_(n) is a 8×1selection vector with all zeros except for the n-th element with value1: ${W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\Y & {- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\{j\; Y} & {{- j}\; Y}\end{bmatrix}}} \right\}$Y ∈ {[e₁  e₅], [e₂  e₆ ], [ e₃  e₇], [e₄  e₈]}.
 3. An apparatus fortransmitting data in a wireless communication system, comprising:circuitry for transmitting a precoding matrix indicator (PMI) to aremote transceiver, wherein the PMI indicates a choice of a precodingmatrix W derived from a matrix multiplication of two matrices W1 and W2from a first codebook C1 and a second codebook C2, respectively, whereinthe first codebook C1 includes at least the following matrices when thenumber of layers N is three or four: $\mspace{20mu}{{B = \begin{bmatrix}b_{0} & b_{1} & \ldots & b_{15}\end{bmatrix}},{\lbrack B\rbrack_{{l + m},\;{l + n}}\; = \; e^{j\;\frac{\;{2\;\pi\;{mn}}}{16}}},\mspace{20mu}{m\; = \; 0},1,2,3}\mspace{14mu}$  n = 0, 1, …  , 15 $X^{(k)} \in \left\{ {{{\begin{bmatrix}b_{{({4\; k})}\;{mod}\mspace{11mu} 16} & {b_{{({{4\; k} + 1})}\;{mod}\mspace{11mu} 16}\mspace{14mu}\ldots} & b_{{({{4\; k} + 7})}\;{mod}\mspace{11mu} 16}\end{bmatrix}:k}\; = \; 0},\; 1,2,3} \right\}$$\mspace{20mu}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1}\; = \;\left\{ {W_{1}^{(0)},\; W_{1}^{(1)},\; W_{1}^{(2)},W_{1}^{(3)}} \right\}},}$wherein the PMI consists of two indices i₁ and i₂ which are periodicallytransmitted within a same set of subframes.
 4. An apparatus fortransmitting data in a wireless communication system, comprising:circuitry for transmitting a precoding matrix indicator (PMI) to aremote transceiver, wherein the PMI indicates a choice of a precodingmatrix W derived from a matrix multiplication of two matrices W1 and W2from a first codebook C1 and a second codebook C2, respectively, whereinthe first codebook C1 includes at least the following matrices when thenumber of layers N is three or four: $\mspace{20mu}{{B = \begin{bmatrix}b_{0} & b_{1} & \ldots & b_{15}\end{bmatrix}},{\lbrack B\rbrack_{{l + m},\;{l + n}}\; = \; e^{j\;\frac{\;{2\;\pi\;{mn}}}{16}}},\mspace{20mu}{m\; = \; 0},1,2,{{3\mspace{20mu} n}\; = \; 0},1,\;\ldots\mspace{14mu},15}$$X^{(k)} \in \left\{ {{{\begin{bmatrix}b_{{({4\; k})}\;{mod}\mspace{11mu} 16} & b_{{({{4\; k} + 1})}\;{mod}\mspace{11mu} 16} & \ldots & b_{{({{4\; k} + 7})}\;{mod}\mspace{11mu} 16}\end{bmatrix}:k}\; = \; 0},\; 1,\; 2,\; 3} \right\}$$\mspace{20mu}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1}\; = \;\left\{ {W_{1}^{(0)},\; W_{1}^{(1)},\; W_{1}^{(2)},\; W_{1}^{(3)}} \right\}},}$and wherein the PMI consists of two indices i₁ and i₂, i₁ periodicallytransmitted within a same set of subframes as a rank indicator feedback,and i₂ periodically transmitted within a different set of subframes fromi₁.
 5. An apparatus for transmitting data in a wireless communicationsystem, comprising: circuitry for forming two or more layers of datastreams wherein each of the data streams consists of modulated symbols;circuitry for generating an 8-by-N precoding matrix based on a precodingmatrix indicator (PMI) feedback from at least one remote receiverwherein the PMI feedback indicates a choice of a precoding matrix Wderived from a matrix multiplication of two matrices W1 and W2 from afirst codebook C1 and a second codebook C2, respectively, wherein thefirst codebook C1 includes at least the following matrices when thenumber of layers N is two: $\mspace{20mu}{{B = \begin{bmatrix}b_{0} & b_{1} & \ldots & b_{31}\end{bmatrix}},{\lbrack B\rbrack_{{l + m},\;{l + n}}\; = \; e^{j\frac{\;{2\;\pi\; n\; m}}{32}}},\mspace{20mu}{m\; = \; 0},1,2,3,{n\; = \; 0},1,\ldots\mspace{14mu},{{31X^{(k)}} \in \left\{ {{{\begin{bmatrix}b_{2\;{kmod}\mspace{11mu} 32} & b_{{({{2\; k} + 1})}\;{mod}\mspace{11mu} 32} & b_{{({{2\; k} + 2})}\;{mod}\mspace{11mu} 32} & b_{{({{2\; k} + 3})}\;{mod}\mspace{11mu} 32}\end{bmatrix}:k}\; = \; 0},1,\;\ldots\mspace{14mu},15,,} \right\}}}$$\mspace{20mu}{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}}$   Codebook  1 : C₁ = {W₁⁽⁰⁾, W₁⁽¹⁾, W₁⁽²⁾, …  , W₁⁽¹⁵⁾}circuitry for precoding the two or more layers of data stream viamultiplication with the 8-by-N precoding matrix where N is the number ofsaid layers; and circuitry for transmitting the precoded layers of datastream to the remote receiver.
 6. The apparatus of claim 5, wherein: thesecond codebook C2 includes at least the following matrices when thenumber of layers N is two and {tilde over (e)}_(n) is a 4×1 selectionvector with all zeros except for the n-th element with value 1:${W_{2} \in C_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{j\; Y_{1}} & {{- j}\; Y_{2}}\end{bmatrix}}} \right\}$$\left( {Y_{1},\; Y_{2}} \right) \in {\left\{ {\left( {{\overset{\sim}{e}}_{1},\;{\overset{\sim}{e}}_{1}} \right),\;\left( {{\overset{\sim}{e}}_{2},\;{\overset{\sim}{e}}_{2}} \right),\;\left( {{\overset{\sim}{e}}_{3},\;{\overset{\sim}{e}}_{3}} \right),\left( {{\overset{\sim}{e}}_{4},\;{\overset{\sim}{e}}_{4}} \right),\;\left( {{\overset{\sim}{e}}_{1},\;{\overset{\sim}{e}}_{2}} \right),\;\left( {{\overset{\sim}{e}}_{2},\;{\overset{\sim}{e}}_{3}} \right),\;\left( {{\overset{\sim}{e}}_{1},\;{\overset{\sim}{e}}_{4}} \right),\;\left( {{\overset{\sim}{e}}_{2},\;{\overset{\sim}{e}}_{4}} \right)} \right\}.}$